Example 1.
First we initialize a 5 dimensional Lie algebra.
Display the Lie bracket multiplication table.
Display the exterior derivatives of the dual 1-forms.
Display the Lie derivatives of the dual 1-forms.
Example 2.
We initialize a 4 dimensional Lie algebra. Instead of using the standard default labels for the basis vectors we use and for the dual 1-forms we use .
Display the Lie bracket multiplication table.
Display the exterior derivatives of the dual 1-forms.
Display the Lie derivatives of the dual 1-forms.
Example 3.
We initialize the quaternions and display the multiplication table.